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A Better Projection Method

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A Better Projection Method

- Despite its utility and ease of use, the extrapolation and ratio methods have some shortcomings. What are some of these?
- 1) Aggregated inputs and outputs 2) No identification of causes of population changesMany refer to the these techniques as a “naïve” methods.
- Improved projections can be generated using a model that improves upon these shortcomings by:1) Using age-sex cohorts as inputs and outputs and2) Investigating changes to the components of population change (Mortality, Fertility, and Migration)
- These improvements to the model lead us to the Cohort-Component Method.

The Cohort Component Model

- This yields the Cohort-Component Method
- Cohort: uniform age, sex, and racial groups
- Component: the three processes resulting in population change; births, deaths, and migration
- The components are largely independent processes that “change by differing amounts at varying times, affecting different segments of the population in diverse ways”. (Klosterman, p. 51)

- Cohort survival: Projects population by age and sex cohorts through the application of birth rates and mortality/survival rates for each. This accounts only for changes due to “natural increase”. No migration component is included.
- Cohort-component model: This method applies birth, death, and migration rates (components) to age-sex cohorts. The difficulty is in generating good migration estimates by the age-sex cohorts. Birth and death information is usually taken from larger civil divisions (state or US rates).
- As we saw in Assignment #1, these methods allow for the creation of population pyramids which illustrate the population for an area by age and sex.

Baby Boomers

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Baby Boom Echo

Advantages of the CC Methods

- Takes into account changes in different components of population (Births, Deaths, Migration)
- Disaggregated inputs and outputs (population figures by age and sex and sometimes race)
- Most widely used technique for projecting populations in the United States
- Big advantage: We now get population size and composition
Disadvantages of the CC Methods

- Complex methods can be difficult to implement and mistakes can more easily be made
- Higher data requirements

The Basics of the Cohort-Component Method

- Age-sex cohorts that cover five year periods (0-4, 5-9, …. 70-74, 75-79, 80+)
- Oftentimes different projections are made for whites, blacks and “other races” because they experience different rates of fertility, mortality, and migration.
- These cohorts are traced over five (or ten) year periods, with the effects of mortality and migration affecting all cohorts and fertility affecting only specific, at-risk groups.
- Data on mortality and fertility come from widely available, published sources. Survival rates and fertility rates are annually computed for the nation, for states, and often for counties.
- Net migration is usually calculated after taking into account the natural increase of a population.

The Mortality Component

- In the CC method, mortality takes the form of “survival rates”. Survival Rates represent the probability that a member of a cohort will survive to become a member of the next cohort at the end of a period of time (usually five years).
- If you have survival rates for a five year period, then the calculation is quite simple:
- Age cohortPop in 1990Survival RatePop in 1995
- Females aged 10-14 285,778 .9988 285,435

- Complications in applying mortality in a CC projection:
- --Need to understand how Life Tables work
- --Be sure whether you have survival rates or mortality rates
- --Understand what time period the rates are for; Is an adjustment necessary (for example, one year rates to five year rates)?
- --Calculating survival rates for the youngest and oldest cohorts
- --Understand what geography the mortality rates come from… does this geography make sense for your study area?

Survival Rates for Selected Age Cohorts

Source: State of Florida 1989-1991 Life Table

- Trend #1: Females generally greater than males
- Trend #2: Whites generally greater than non-whites

Source: State of Florida 1989-1991 Life Table

Leon County 1990

White Females

Leon County 1995

White Females

New Babies

Mortality and Life Tables

- Life Tables are constructed by demographers. They are statistical tables that summarize a population’s mortality characteristics. Example: United States Life Table, 2000
- Understanding Life Tables
- Column 1: Age Interval (x to x+1)
- Column 2: Mortality Rate (Probability of Dying)
- Column 3: Number Surviving to the beginning of the age cohort
- Column 4: Number Dying between x and x+1
- Column 5: Total number of persons alive in the “Stationary Population” for a given age cohort (the average number alive at the beginning and end of a year for that cohort)
- Column 6: Total person years to be lived for this and all subsequent cohorts
- Column 7: Average number of years of life remaining to persons of exact age x.
- We use life tables to calculate Survival Rates.

Calculating 1 Year Survival RatesSR= Stable Pop C2/Stable Pop C1

SR Yrs 1-2= 99,353 / 99,454 = .99898

Calculating 5 Year Survival RatesSR= Stable Pop C2/Stable Pop C1

SR Yrs 0-4= 495,668/496,490 = .998344

SR Yrs 5-9 = 495,268/495,668 = .999193

Projecting Mortality Rates

- Applying the mortality component in a cohort component analysis is relatively straightforward.
- However, although you may have excellent data on mortality rates for a given time (say, 2000), the analyst must decide what to do about future mortality rates. What are the various options when considering future mortality rates?

1) Do Nothing, Assume Constant Mortality Rates2) Use Extrapolation to Project Mortality Rates3) Use a Synthetic Projection that looks at the rates of change in Mortality Rates in a Pattern Area (like the US) --Constant Share, Shift Share techniques

The Fertility Component

- In the CC method, Fertility is incorporated as infants born to women in the fertile age cohorts who survive to become members of the projected population in the first cohort.
- The convention is to: 1) calculate the number of births expected 2) allocate the births to male or female using the sex ratio and 3) then calculate the number that will survive to the next cohort
- Complications in applying fertility in a CC projection 1. Single year, small area fertility rates should not be used for projecting the number of births. (Variability, “contamination”) 2. Must determine ratio for male-female births (aka sex ratio) (105.7(W), 102.3 (B)) 3. Time period issues: We may need to convert one year rates to five year rates. (5 * one year rate)

The Fertility Component: Calculating Births

- There are a two primary methods for calculating the number of births over a five year period. 1) CW Ratio and 2) ASBR
- 1) Child-woman ratio: Calculate the ratio of “at-risk women” to children aged 0-4 for a five year period (or children aged 0-4, 5-9 for a ten year period). Then apply this ratio in the future, or adjust as necessary. For example:
- Women 10-49 in 1995:2,718,192(1)
- Children 0-4 in 1995: 736,285(2)
- CWR = (1) / (2) = .270873
- We could assume that the CWR for the next five years would be the same. Then, using the number of at-risk women from Census 2000 we can project the number of births expected from this group.
- We would also apply the sex ratio to determine the number of males and females in the 0-4 age cohort.

The Fertility Component: Calculating Births

- The second method for calculating the number of births over a five year period is the use of age-specific birth rates.
- 2) Age-specific birth rates: This is simply the number of births to an age cohort divided by the number of women in that age cohort, multiplied by 1,000 (births per 1,000 women)
- Number of Births Women Aged 20-24 = 938
- Midyear Female Pop Aged 20-24= 7,691
- ASBR = 938/7,691 * 1000 = 121.96 births per 1000 women
- The state Office of Vital Statistics calculates age specific birth rates for the total population, whites, and non-whites. These rates are published in Florida Vital Statistics.
- We can use these pre-calculated rates and apply them to the appropriate age cohorts to estimate and project the number of births.
- However, we must remember to take into account the “average population” for each cohort. (See Klosterman pages 80-86.)

Source: State of Florida Vital Statistics, 1993

Putting Mortality and Fertility Together